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Page No 33:

Question 1:

If,
find the values of x
and y.

Answer:

It
is given that.

Since the
ordered pairs are equal, the corresponding elements will also be
equal.

Therefore,
and.

∴ x
= 2 and y
= 1

Page No 33:

Question 2:

If
the set A has 3 elements and the set B = {3, 4, 5}, then find the
number of elements in (A × B)?

Answer:

It
is given that set A has 3 elements and the elements of set B are 3,
4, and 5.

⇒ Number
of elements in set B = 3

Number
of elements in (A × B)

=
(Number of elements in A) × (Number of elements in B)

=
3 × 3 = 9

Thus,
the number of elements in (A × B) is 9.

Page No 33:

Question 3:

If
G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

Answer:

G
= {7, 8} and H = {5, 4, 2}

We
know that the Cartesian product P × Q of two non-empty sets P
and Q is defined as

P
× Q = {(p,
q):
p∈
P, q∈
Q}

∴G
× H = {(7, 5), (7, 4), (7, 2), (8, 5), (8, 4), (8, 2)}

H
× G = {(5, 7), (5, 8), (4, 7), (4, 8), (2, 7), (2, 8)}

Page No 33:

Question 4:

State whether each of the following statement are true or false. If the statement is false, rewrite the given statement correctly.

(i) If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.

(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x∈ A and y∈ B.

(iii) If A = {1, 2}, B = {3, 4}, then A × (B∩ Φ) = Φ.

Answer:

(i) False

If P = {m, n} and Q = {n, m}, then

P × Q = {(m, m), (m, n), (n,m), (n, n)}

(ii) True

(iii) True

Page No 33:

Question 5:

If
A = {–1, 1}, find A × A × A.

Answer:

It
is known that for any non-empty set A, A × A × A is
defined as

A
× A × A = {(a,
b,
c):
a,
b,
c
∈
A}

It
is given that A = {–1, 1}

∴ A
× A × A = {(–1, –1, –1), (–1, –1,
1), (–1, 1, –1), (–1, 1, 1),

(1,
–1, –1), (1, –1, 1), (1, 1, –1), (1, 1, 1)}

Page No 33:

Question 6:

If
A × B = {(a,
x),
(a,
y),
(b,
x),
(b,
y)}.
Find A and B.

Answer:

It
is given that A × B = {(a,
x),
(a,y),
(b,
x),
(b,
y)}

We
know that the Cartesian product of two non-empty sets P and Q is
defined as P × Q = {(p,
q):
p∈
P, q∈
Q}

∴ A
is the set of all first elements and B is the set of all second
elements.

Answer:

The domain of R is the set of all first elements of the ordered pairs in the relation.

∴Domain of R = {1, 2, 3, 4}

The whole set A is the codomainof the relation R.

∴Codomain of R = A = {1, 2, 3, …, 14}

The range of R is the set of all second elements of the ordered pairs in the relation.

∴Range of R = {3, 6, 9, 12}

Page No 36:

Question 2:

Define
a relation R on the set N
of natural numbers by R = {(x,
y):
y
= x
+ 5, x
is a natural number less than 4; x,
y∈N}.
Depict this relationship using roster form. Write down the domain and
the range.

Answer:

R
= {(x,
y):
y
= x
+ 5, x
is a natural number less than 4, x,
y∈N}

The
natural numbers less than 4 are 1, 2, and 3.

∴R
= {(1, 6), (2, 7), (3, 8)}

The
domain of R is the set of all first elements of
the ordered pairs in the relation.

∴ Domain
of R = {1, 2, 3}

The
range of R is the set of all second elements of
the ordered pairs in the relation.